Bernard Grofman and Reuben
Kline, "How many political parties are there, really? A new
measure of the ideologically cognizable number of
parties/party groupings," Party Politics 18 (July,
2012), 523-544. [Available at http://ppq.sagepub.com/content/vol18/issue4/
]

First paragraph:
How many political parties are there in the parliament of
country Q? How many parties contested the election in which
that parliament was elected? To anyone who has not thought
much about these questions, they seem rather trivial
problems - requiring for their answer only the kind of
counting you learned to do in kindergarten. Yet, they are
far from simple once we recognize that, as social
scientists, what we want to do is to operationalize the
number of parties at the electoral and parliamentary level
in a way that will allow us to forge theoretical links
between these variables and other key features of a
country's politics. After reviewing the two most important
efforts to address such questions: the Laakso-Taagepera
index (LT index) of the effective number of parties (Laakso
and Taagepera, 1979) and the Banzhaf power score
modification of the LT index to take into account party
decisiveness in a parliamentary weighted voting game (Dumont
and Caulier, 2003; Grofman, 2006; Kline, 2009), which we
will abbreviate the LTB index, we offer a new method of
counting parties that integrates effective size
considerations with party locations in policy space to
develop what may be thought of as a measure of the
ideologically cognizable number of parties/ party
ideological groupings.

Figures and
Tables:

Figure 1. Hypothetical Party Locations in a Three
Party System

Table 1. Dislocation for the Hypothetical Party
Configuration in Figure 1(a)

Table 2. Canadian Paty System Data, 2004
Election

Table 3. Slovenian Paty System Data, 1996
Election

Last Paragraph:
With appropriate data, the methodology we have used can be
applied to many more countries, just as is true for the
Dalton (2008) polarization measure, and it need not be
restricted to one-dimensional representations of party
space. It is increasingly common in studies of party systems
or electoral competition to report a time series for
Laakso-Taagepera values at the vote and/or seat level. Our
methodology can also be applied to making sense of changes
in party constellations over time in away that is usefully
complementary to the more standard approaches of simply
counting changes in seat-winning parties or in the effective
number of parties.Wehope that this articlewill inspire the
development of similar time series on changes in the
ideological bloc structure of party competition.